Some of the things you can do with the GrassmannAlgebra software. You can: * Set up your own space of any dimension and metric. The default is a 3D Euclidean * Work basis-free or with a basis * Declare your own scalar symbols * Declare your own vector symbols: * Apply Grassmann operations. A Grassmann operation is any of: the complement operation and the six product operations: the exterior, regressive, interior, generalized Grassmann, hypercomplex and Clifford products. * Manipulate Grassmann expressions and numbers. A Grassmann expression is either a scalar, a Grassmann variable, or the result of a sequence of Grassmann operations or sums on Grassmann expressions. A Grassmann number is a Grassmann expression expressed as a linear combination of basis elements. * Compute the grade of any Grassmann expression. * Query the attributes of any expression. * Extract components of different types
A. Lasenby, C. Doran, und S. Gull. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 356 (1737):
487--582(1998)
E. Bayro corrochano, und J. Lasenby. Proceedings of Europe-China Workshop on Geometric Modeling and Invariants for Computer Vision, Ed. Roger Mohr and Wu Chengke, Seite 143--149. (1995)
F. McRobie, und J. Lasenby. IUTAM-IASS Symposium on Deployable Structures: Theory and Applications, Volume 80 von Solid Mechanics and Its Applications, Springer Netherlands, (2000)
S. Buchholz, E. Hitzer, und K. Tachibana. IN: PROC. JOINT 4TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS AND 9TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (SCIS AND ISIS 2008, (2008)
A. Lasenby, C. Doran, und S. Gull. (2004)cite arxiv:gr-qc/0405033Comment: 112 pages, 6 figures. Published in Phil. Trans. R. Soc. Lond. A 356, 487-582 (1998). Revised version with some corrections and improvements.
J. Lasenby, S. Gamage, und M. Ringer. Algebraic Frames for the Perception-Action Cycle, Volume 1888 von Lecture Notes in Computer Science, Springer Berlin Heidelberg, (2000)
H. Li, L. Dong, C. Shao, und L. Huang. Proceedings of the conference on Applied Geometric Algebra in Computer Science and Engineering, Seite 195-204. (2015)
L. Couturat. Translated by Donald Rutherford and R. Timothy Monroe,, (1901 / 2012)Accessed online at http://philosophyfaculty.ucsd.edu/faculty/rutherford/Leibniz/couturatcontents.php.
L. Falcon-Morales, und E. Bayro-Corrochano. Robotics and Automation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on, Seite 2627-2632. (Mai 2006)
D. Hestenes, H. Li, und A. Rockwood. Geometric Computing with Clifford Algebras, Kapitel New Algebraic Tools for Classical Geometry, Springer-Verlag, London, UK, UK, (2001)
R. Krasauskas, und S. Zube. Proceedings of 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Weimar, Germany, (2011)
D. Hestenes. Clifford Algebras and their Applications in Mathematical Physics, Volume 55 von Fundamental Theories of Physics, Springer Netherlands, (1993)
G. Sobczyk. Clifford Algebras and their Applications in Mathematical Physics, Volume 47 von Fundamental Theories of Physics, Springer Netherlands, (1992)
D. Hestenes, und G. Sobczyk. D. Reidel ; Distributed in the U.S.A. and Canada by Kluwer Academic Publishers, Dordrecht; Boston; Hingham, MA, U.S.A., (1984)